Result Based Texture Mapping
Make sure all the objects have a UV map (it doesn't have to be a useful one). 

If you have a large number of objects which don't a UV map, unwrap one of them (any projection will do) and then select them all (with the unwrapped one active) and press CtrlL > Transfer UV maps. Even if the objects don't have the same vertex order, this will be fine as the UV map is overwritten later.
Simulate/animate the objects and go to the last frame.
Select all the objects, add a UV project modifier and set the camera as the projection object, select the UV map, and press CtrlL> Modifiers:



This will project the UVs from the camera unto the objects. If you move the camera in textured view you can see this in real time.
Still on the last frame with all the objects selected, press AltC > Convert to mesh to apply all the modifiers (and make the UV maps stay in the state they are in).


Result (click on it for html5 version):